The answer to this question can be found right at the start of Chapter 14. Briefly, what the Giver says is that he and Jonas have to hold the memories (even if they are painful) because the memories give them wisdom. This wisdom can be used to help the Community when that becomes necessary.
For example, the Giver says, the wisdom that he has gained from the memories tell him that overpopulation is bad. He used that wisdom to help the Community some time previously when the Elders were thinking about whether to have each birth mother have more kids.
So the Giver and Jonas are supposed to be the wisdom of the Community, remebering things that might be of help at some point.